Flags wave at the last night of the BBC Proms last year. Photograph: Chris McAndrew/Camera Press

It has been 30 years since a BBC Prom was cancelled because of industrial action. But now the annual music festival could be hit by a strike as the BBC's director general, Mark Thompson, faces the biggest internal crisis of his tenure. Anger at senior executives' wages and concern over plans to change the BBC's pension scheme have created a pay and pensions storm. From union posters showing executives with their pockets stuffed with cash to the sabotage of a live in-house broadcast from Thompson by prefacing it with a test card reading "Mark Thompson pensions = screw you", the mood is darkening.

As one BBC staff member says: "There is resentment regarding the pay gap between top and rank-and-file staff. The senior directors just have no idea about the depth of feeling – some of them seem to be removed from the PR disasters that have occurred recently, such as Peter Salmon not relocating to Salford, and there are concerns about a lack of leadership."

This is not news to Thompson, who has tried to stem complaints with moves such as senior executives volunteering to work for free one month each year for two years, and undoubtedly he will try to use Friday's MacTaggart lecture at the MediaGuardian Edinburgh international television festival to rally his troops. But the most immediate potential casualty is the hugely popular and successful Proms season. Staff have been balloted by unions and if they vote for industrial action the first date scheduled for a strike is 9 September, two days before the Proms end.

Angry audience

The last time industrial action disrupted the concerts was in 1980, when the first night was cancelled following walkouts over plans to cut five orchestras and 172 jobs. Coincidentally 9 September is when Roger Wright, the Proms director and Radio 3 controller, is due to do a live question and answer session at the festival. The amiable Wright seems unfazed by the prospect of what the union Bectu predicts could be "a blank screen – and no one in the Albert Hall, except a very angry audience."

Erudite and self- effacing, Wright is remarkably jovial considering his workload. In a room Wright calls the bunker, by a piano he likes to use, he tells me this year's Proms is going well. "It would be invidious of me to start picking any single one out. But the opening weekend captured people's imagination. As a statement of intent, particularly off the back of the BBC's opera programming, to start with Mahler's Symphony No 8 then [Wagner's] Die Meistersinger and [Verdi's] Simon Boccanegra. To have that for £5 you get a lot. I think that is actually what the Proms is about. It's why the brand is so strong."

The Proms cost £9m – funded by £6m from the licence fee and the rest from ticket sales. "The licence fee means you can keep the quality high and the ticket price low, which is the magic formula," says Wright. The range means one night there is a Doctor Who Prom, the next the European Union Youth Orchestra and they are all packed, often with young audiences. "There's so much every night. If there's a question mark for demographics for classical music the Proms is always held up, partly because of price, partly because of the perceived accessibility and informality."

The spirit of Lord Reith is alive and well in Wright: "When you get people saying: 'I came to Radio 3 because of Andy Kershaw and now I listen to Composer of the Week,' I think 'Hurrah, public service broadcasting is alive and well.' That sort of serendipity is in the end the thing that's still vital, it's curiosity. I hope that curiosity is at the heart of the Proms and Radio 3 and performing groups. People can fall into the arms of familiar music but having got them there you want to take them to different places." He adds: "The most important thing is audiences care and feel a great sense of ownership about BBC services and they care about the Proms."

Ticket exclusive

The good news is that the £5 ticket prices will stay at the same level next year, Wright reveals: "They've been that price for five or six years now. They will remain – we haven't told anyone that, but given we've just told you, we'd better make that policy!"

But what of Radio 3? The latest Rajar figures revealed a year-on-year fall of around 8% to an average weekly audience of 1.86 million. Although previously Wright has said he "worries" about Rajars, he seems unfazed: "Given that Rajar figures only come out every quarter – and thank goodness we don't have the terror of overnights – there's always the hope and desire that the figures are OK and to that extent they are only one measure of success. They're an important measure, which is why one's keen to get them. But it's been 2 million or thereabouts for the last 10 years. And we're in a very strong position. Radio suits the business of lives, it's a flexible medium."

Like the reprieved 6 Music, Radio 3 supports live performance, with 57% of its music not pre-recorded. Wright also highlights the return of Kershaw to Radio 3 in the autumn, "in the way only Andy can", with an ambitious tie-up with BBC1's anthropological global journey Human Planet called Music Planet.

What about any changes to Radio 3's schedule? Nothing is on the cards but Wright says: "You always look to see what might have run its course. One of the things that has worked is to make the schedule as navigable as possible." As he says, Radio 3 is "a radio station, not a university of the air". Some listeners have objected that Wright has made the breakfast programme sound more like, well, a breakfast programme. "I think 'Yippee' when I hear that, because that's what it is," he says.

Wright is discussing with the BBC Trust the inclusion of the Proms and performing groups in Radio 3's service licence - currently they are not, and this could help protect against budget cuts. The bulk of its £51m budget goes into performances and it has £350,000 to commission new music, making it a major player in the classical music world's future. But with the corporation enduring voluntary redundancies and cuts, it still has to prove that it is being as "cost-effective as possible", he says.

The BBC will be making the case for the licence fee over the coming months, and Radio 3 and the Proms are gems to polish in its crown. But Wright, who is renowned for trying to open up music to a wider audience, is careful to ensure they are savoured as national treasures rather than antiques. His latest move to bring in new listeners is an award-winning TV promo that features people hearing Radio 3 when they walk on a giant red spot.

Many Radio 3 listeners also listen to Radio 4, but Wright is casting his net wider with initiatives such as a search to find the nation's favourite aria, which captured the public's imagination this year. "We're trying to get people to sample the station and get our regular listeners listening for longer. It's a simple message." While some Radio 3 devotees may turn up their noses at such moves to make the station more welcoming to the uninitiated, Wright is keen to break down barriers: "I'm uncomfortable with the business of musical hierarchies."

A keen cricket fan, he deals with most questions with a straight bat, even the inevitable one about his expenses. During the Proms season he stays overnight in a London hotel – and his bills and taxi receipts have made the headlines. He explains: "It's perfectly right and proper that we're as transparent as possible. I'm a public servant and as part of that I have my expenses made public every quarter. I do live a certain way outside London and doing both Proms and Radio 3 there are a lot of late nights and early mornings.

"I'm not going to camp in Hyde Park, it would probably take me too long to put a tent up anyway. I do sometimes take the bus and the tube, however that can sometimes take a very long time and I don't claim back those tickets. Last night I got home at 1.50am and had to be back in the Royal Albert Hall by 9.15am. I don't want to book central cabs because if you are waiting for Plácido Domingo to sign around 4,000 autographs there's going to be some waiting time. All I can do is have my integrity. Am I complaining about having my expenses public, though? No."

The only time the shutters come down is when I ask if there is a contingency plan should the Proms, which are aired live, be hit by industrial action next month. If there is a plan, Wright is not revealing it: "There's a consultation going on. There have been strikes and industrial actions before and we'll deal with the situation in the same way. It's just what you deal with if big live events don't happen for some reason. All you can do is keep talking to people and making sure you're open."

Interviewers rarely get much out of Wright if they ask him about his future. With a career that so far has spanned the BBC, the commercial recording industry and performance groups, what does he want to do next? "I don't think about my career in that sense – it's not something I think about. I'm just very happy doing what I do now. As for my ambitions, well, to be on Test Match Special." And presumably to ensure this year's Last Night of the Proms is remembered as an Ode to Joy and not a Work to Rule Britannia.